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DUMET Medical DUMET Medical Solved Paper-2009

  • question_answer
    Two stars of mass \[{{m}_{1}}\] and \[{{m}_{2}}\] are parts of a binary star system. The radii of their orbits are \[{{r}_{1}}\] and \[{{r}_{2}}\] respectively, measured from the centre of mass of the system. The magnitude of gravitational force \[{{m}_{1}}\] exerts on m, is

    A) \[\frac{{{m}_{1}}{{m}_{2}}G}{{{({{r}_{1}}+{{r}_{2}})}^{2}}}\]

    B) \[\frac{{{m}_{1}}G}{{{({{r}_{1}}+{{r}_{2}})}^{2}}}\]

    C) \[\frac{{{m}_{2}}G}{{{({{r}_{1}}+{{r}_{2}})}^{2}}}\]

    D) \[\frac{({{m}_{1}}+{{m}_{2}})}{{{({{r}_{1}}+{{r}_{2}})}^{2}}}\]

    Correct Answer: A

    Solution :

     Gravitational force between two bodies of mass \[F=\frac{G{{m}_{1}}{{m}_{2}}}{{{d}^{2}}}\] where d is the distance between the two masses. Here, \[d={{r}_{1}}+{{r}_{2}}\] \[\therefore \] \[F=\frac{G{{m}_{1}}{{m}_{2}}}{{{({{r}_{1}}+{{r}_{2}})}^{2}}}\]


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